11/03/2022

Cesar Poma presents a thesis on curve-induced fibrations.

From the beginning of his school career until graduation in Peru, Cesar Augusto Hilario Poma had a strong interest in mathematics, but did not think about pursuing a career in the field. It was only while studying electronic engineering at the National University of Engineering, in Lima, that he decided to change course. Next Monday (14), Poma will present his doctoral thesis “Fibrations by singular curves of arithmetic genus three in characteristic two”. Supervised by researcher Karl-Otto Sthör, the presentation will be broadcast at 1 pm on IMPA's YouTube channel .

“Although I was good at math in school, I never considered it as a future career, perhaps due to misinformation. It was a fun and competitive subject, but I didn't know the formal aspects of it, nor did I know it was possible to make a living as a mathematician,” explained the doctoral student.

He became interested in the subject during his undergraduate engineering classes. “In engineering school, we mainly learn to use mathematics as a tool, but it is not, in itself, the object of study. I kept wondering why, for example, when we calculate a double or triple integral, the order of integration can be reversed, but these kinds of questions weren't relevant in the course.”

Poma has been at IMPA since 2016 when he began his master's degree. He became acquainted with the institute during his undergraduate studies and subsequently decided to take the Summer Course. "At my university, we used books from IMPA's Euclides project, especially Elon Lages Lima's book on Real Analysis, which was famous there. In addition, several professors had doctorates or some connection with IMPA," he said.

The doctoral student discovered an interest in algebraic geometry and ended up focusing on the study of fibrations by curves. “To get an intuitive idea, one can think of a mathematical object as a real line. Each point on this object has a curve, and all these curves are compatible. When we work on the field of real or complex numbers, most of these curves are smooth. But the situation changes if we work in a more abstract context: on fields of positive characteristic. In this context, it is possible that most of the curves are not smooth,” he explained.

In her free time, Poma usually enjoys outdoor activities or going to the movies. But a good part of her time is dedicated to her area of interest. “In school, mathematics was that fun subject that always brought challenging questions. At university, mathematics acquired a beauty I hadn't imagined. I think it's like a puzzle: a set of pieces that fit together very well. Mathematics is also poetry: I've seen proofs that are beautiful in their simplicity. And it has given me many things in life. I've met many people and experienced many cultures thanks to it,” she concluded.